📖 The story
The Hoffmann family has $25,000 sitting in a savings account and is thinking of investing it at 6 % instead. They want to know when the amount will have doubled.
ℹ Lump-sum investment, annual compounding, no additional deposits.
Topics › Saving & Compound Interest › When does the savings double?
Easy
Saving & Compound Interest
When does the savings double?
Change any number and press "Calculate" – or use "Type in" on the right to watch it entered.
What you learn
Anyone who postpones a purchase and invests the money instead eventually finances it from the earnings alone – patience plus compound interest replaces a loan.
In short: At 6 % doubling takes about twelve years – every extra percentage point shortens it noticeably.
Formula
n = ln((FV + R/i)/(K0 + R/i)) / ln(1+i)
With the example numbers
n = ln((FV + R/i)/(K₀ + R/i)) / ln(1+i) ⇒ 11,90 Jahre
How to read the formula
The unknown is the exponent n. Because n is in the power, you can only get at it via the logarithm: n = ln(ratio)/ln(1+i). The logarithm is the inverse of raising to a power and answers the question "how often must I multiply by q until the target is reached".
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